Precalculus Examples

$3 (e^{1 + t}) = 2$

Step 1

Simplify.

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Step 1.1

Multiply $3$ by $e^{1 + t}$ .

$3 e^{1 + t} = 2$

Step 1.2

Divide each term in $3 e^{1 + t} = 2$ by $3$ .

$\frac{3 e^{1 + t}}{3} = \frac{2}{3}$

Step 1.3

Reduce by cancelling the common factors.

$e^{1 + t} = \frac{2}{3}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(e)$ of the right side $(\frac{2}{3})$ equals the exponent $(1 + t)$ .

$\log_{e} (\frac{2}{3}) = 1 + t$